Question

In: Statistics and Probability

The table to the below contains observed values and expected values in parentheses for two categorical​...

The table to the below contains observed values and expected values in parentheses for two categorical​ variables, X and​ Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts​ (a) and​ (b) below.

X1

X2

X3

Y1

34

40

55

36.86

43.24

48.91

Y2

18

21

14

15.14

17.76

20.09

(a) Compute the value of the​ chi-square test statistic. ​(Round to three decimal places as​ needed.)

X 2/0=

(b) Test the hypothesis that X and Y are independent at the alpha equals 0.01 level of significance.

H0​: mu x = Ex and mu y = Ey; H1: mu x does not = Ex or mu y does not = Ey

H0​: Y category and X category are independent; H1​: The Y category and X category are dependent.

H0​: Y category and X category are dependent; H1​: The Y category and X category are independent.

H0​: Y category and X category have equal proportions; H1​: The proportions are not equal.

(c) What range of​ P-values does the test statistic correspond​ to? The​ P-value is ?

(d) Should the null hypothesis be​ rejected?

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